<IUT国際会議 2シリーズ> http://www.kurims.kyoto-u.ac.jp/~bcollas/IUT/IUT-schedule.html RIMS Promenade in Inter-Universal Teichmuller Theory Org.: Collas (RIMS); Debes, Fresse (Lille). The seminar takes place every two weeks on Thursday for 2 hours by Zoom 17:30-19:30, JP time (9:30-11:30, UK time; 10:30-12:30 FR time) ? we refer to the Programme for descriptions of the talks and associated references. http://www.kurims.kyoto-u.ac.jp/~bcollas/IUT/documents/RIMS-Lille%20-%20Promenade%20in%20Inter-Universal%20Teichm%C3%BCller%20Theory.pdf
https://arxiv.org/pdf/2004.13108.pdf PROBABILISTIC SZPIRO, BABY SZPIRO, AND EXPLICIT SZPIRO FROM MOCHIZUKI’S COROLLARY 3.12 TAYLOR DUPUY AND ANTON HILADO Date: April 30, 2020. P14 Remark 3.8.3. (1) The assertion of [SS17, pg 10] is that (3.3) is the only relation between the q-pilot and Θ-pilot degrees. The assertion of [Moc18, C14] is that [SS17, pg 10] is not what occurs in [Moc15a]. The reasoning of [SS17, pg 10] is something like what follows: P15 (2) We would like to point out that the diagram on page 10 of [SS17] is very similar to the diagram on §8.4 part 7, page 76 of the unpublished manuscript [Tan18] which Scholze and Stix were reading while preparing [SS17]. References [SS17] Peter Scholze and Jakob Stix, Why abc is still a conjecture., 2017. 1, 1, 1e, 2, 7.5.3 ( http://www.kurims.kyoto-u.ac.jp/~motizuki/IUTch-discussions-2018-03.html ) [Tan18] Fucheng Tan, Note on IUT, 2018. 1, 2 つづく
なお "[SS17] Peter Scholze and Jakob Stix, Why abc is still a conjecture., 2017."は、2018の気がする ”[Tan18] Fucheng Tan, Note on IUT, 2018. 1, 2”が見つからない。”the unpublished manuscript [Tan18]”とはあるのだが(^^ 代わりに、ヒットした下記でも、どぞ (2018の何月かが不明だが、2018.3のSS以降かも)
http://www.kurims.kyoto-u.ac.jp/~motizuki/Tan%20---%20Introduction%20to%20inter-universal%20Teichmuller%20theory%20(slides).pdf Introduction to Inter-universal Teichm¨uller theory Fucheng Tan RIMS, Kyoto University 2018 To my limited experiences, the following seem to be an option for people who wish to get to know IUT without spending too much time on all the details. ・ Regard the anabelian results and the general theory of Frobenioids as blackbox. ・ Proceed to read Sections 1, 2 of [EtTh], which is the basis of IUT. ・ Read [IUT-I] and [IUT-II] (briefly), so as to know the basic definitions. ・ Read [IUT-III] carefully. To make sense of the various definitions/constructions in the second half of [IUT-III], one needs all the previous definitions/results. ・ The results in [IUT-IV] were in fact discovered first. Section 1 of [IUT-IV] allows one to see the construction in [IUT-III] in a rather concrete way, hence can be read together with [IUT-III], or even before. S. Mochizuki, The ´etale theta function and its Frobenioid-theoretic manifestations. S. Mochizuki, Inter-universal Teichm¨uller Theory I, II, III, IV.
http://www.kurims.kyoto-u.ac.jp/daigakuin/Tan.pdf 教員名: 譚 福成(Tan, Fucheng) P-adic Hodge theory plays an essential role in Mochizuki's proof of Grothendieck's Anabelian Conjecture. Recently, I have been studying anabeian geometry and Mochizuki's Inter-universal Teichmuller theory, which is in certain sense a global simulation of p-adic comparison theorem.
http://www.kurims.kyoto-u.ac.jp/~bcollas/IUT/documents/RIMS-Lille%20-%20Promenade%20in%20Inter-Universal%20Teichm%C3%BCller%20Theory.pdf Research Institute for Mathematical Sciences - Kyoto University, Japan PROMENADE IN INTER-UNIVERSAL TEICHMULLER THEORY - 復元 Online Seminar - Algebraic & Arithmetic Geometry Laboratoire Paul Painleve - Universite de Lille, France Version 1 ? ε - 09/10/2020
http://www.kurims.kyoto-u.ac.jp/~bcollas/IUT/IUT-references.html Promenade in Inter-Universal Teichmuller Theory Org.: Collas (RIMS); Debes, Fresse (Lille). The Programme of the seminar contains a selection of ~30 references with respect to (1) Diophantine Geometry, (2) IUT Geometry, and (3) Anabelian Geometry. We indicate some links towards the key opuses as well as some complementary notes and proceedings.
(>>6より) http://www.kurims.kyoto-u.ac.jp/~motizuki/Explicit%20estimates%20in%20IUTeich.pdf Explicit Estimates in Inter-universal Teichmuller Theory. PDF NEW!! (2020-11-30) いわゆる南出論文
Abstract We also obtain an explicit estimate concerning “Fermat’s Last Theorem” (FLT) - i.e., to the effect that FLT holds for prime exponents > 1.615 * 10^14 - which is sufficient to give an alternative proof of the first case of Fermat’s Last Theorem.
2.IUTの新たな方向への発展:例えば下記”random measurable sets”とか、Joshi論文 Dupuy論文の下記(”based on the notion of random measurable sets”) https://arxiv.org/pdf/2004.13108.pdf PROBABILISTIC SZPIRO, BABY SZPIRO, AND EXPLICIT SZPIRO FROM MOCHIZUKI’S COROLLARY 3.12 Abstract. All of these inequalities are derived from an probabilistic version of [Moc15a, Corollary 3.12] formulated in [DH20b] based on the notion of random measurable sets. Joshi論文 https://arxiv.org/pdf/2003.01890.pdf On Mochizuki’s idea of Anabelomorphy and its applications Kirti Joshi April 24, 2020 https://arxiv.org/pdf/2010.05748.pdf Untilts of fundamental groups: construction of labeled isomorphs of fundamental groups Kirti Joshi October 13, 2020 P2”My thanks are due to Peter Scholze, and also to Yuichiro Hoshi, Emmanuel Lepage, and Jacob Stix, for promptly providing comments,suggestions or corrections.”